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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1972, Volume 12, Issue 2, Pages 197–204 (Mi mz9868)

V. E. Govorov

Moscow Institute of Electronic Machinery

Abstract: We study the growth in the number of dimensions $d_n$ of the homogeneous component of a graded algebra with a finite number of defining relations and generators for the Poincaré series $\sum d_nx^n$. It is proved that if the defining relations are words, the Poincaré series is a rational function. In the general case inequalities are proved linking the number of dimensions $d_n$ with the number of generators defining relations and their degree.

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English version:
Mathematical Notes, 1972, 12:2, 552–556

Bibliographic databases:

UDC: 519.4

Citation: V. E. Govorov, “Graded algebras”, Mat. Zametki, 12:2 (1972), 197–204; Math. Notes, 12:2 (1972), 552–556

Citation in format AMSBIB
\Bibitem{Gov72} \by V.~E.~Govorov \paper Graded algebras \jour Mat. Zametki \yr 1972 \vol 12 \issue 2 \pages 197--204 \mathnet{http://mi.mathnet.ru/mz9868} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=318199} \zmath{https://zbmath.org/?q=an:0239.16002} \transl \jour Math. Notes \yr 1972 \vol 12 \issue 2 \pages 552--556 \crossref{https://doi.org/10.1007/BF01095017} 

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This publication is cited in the following articles:
1. R. I. Grigorchuk, “Degrees of growth of finitely generated groups, and the theory of invariant means”, Math. USSR-Izv., 25:2 (1985), 259–300
2. V. E. Govorov, “Codes and homology”, Math. USSR-Sb., 52:1 (1985), 275–282
3. I. K. Babenko, “Problems of growth and rationality in algebra and topology”, Russian Math. Surveys, 41:2 (1986), 117–175
4. V. A. Ufnarovskii, “On the use of graphs for computing a basis, growth and Hilbert series of associative algebras”, Math. USSR-Sb., 68:2 (1991), 417–428
5. D. I. Piontkovskii, “Hilbert series and their relations in algebras”, Russian Math. Surveys, 53:6 (1998), 1360–1361
6. D. I. Piontkovskii, “Hilbert series and relations in algebras”, Izv. Math., 64:6 (2000), 1297–1311
7. D. I. Piontkovskii, “On graded algebras of global dimension 3”, Izv. Math., 65:3 (2001), 557–568
8. A. M. Shur, “O vychislenii parametrov i tipov povedeniya kombinatornoi slozhnosti regulyarnykh yazykov”, Tr. IMM UrO RAN, 16, no. 2, 2010, 270–287
9. Dilber Koçak, “Finitely presented quadratic algebras of intermediate growth”, Algebra Discrete Math., 20:1 (2015), 69–88
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